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#72306382

• p-group
• nilpotent
• supersolvable
• solvable
• monolithic
• monomial
• stem

Aliases

No aliases for this group.

Subgroups

2745 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 64 points:

(1,2)(3,14)(4,20,23,42,21,57,26,41)(5,27,28,43)(6,12)(7,13)(8,15)(9,24,37,60,39,25,38,29)(10,30,11,31)(16,47,48,63,22,58,50,64)(17,51,18,54)(19,45)(32,44)(33,59,61,52,36,49,62,55)(34,56,40,53)(35,46);(3,15)(4,21)(5,28)(8,14)(10,11)(16,22)(19,46)(20,57)(23,26)(27,43)(30,31)(35,45)(41,42)(47,58)(48,50)(63,64);(1,3)(2,8)(4,22)(5,18)(6,19)(7,15)(9,36)(10,40)(11,34)(12,35)(13,14)(16,21)(17,28)(20,58)(23,50)(24,49)(25,59)(26,48)(27,51)(29,52)(30,56)(31,53)(32,46)(33,39)(37,62)(38,61)(41,63)(42,64)(43,54)(44,45)(47,57)(55,60);(1,4,5,29)(2,9,11,42)(3,16,18,55)(6,23,31,24)(7,21,28,60)(8,33,34,63)(10,41,13,39)(12,37,27,57)(14,36,40,64)(15,22,17,52)(19,48,53,59)(20,44,38,43)(25,32,26,30)(35,61,51,58)(45,62,54,47)(46,50,56,49)

Polycyclic presentation:

2^10|a^2=e,d^2=eg,e^2=i,f^2=j,g^2=j,h^2=j,c^a=cij,c^b=cij,d^a=df,d^b=dfgj,d^c=dj,e^d=eh,f^a=fh,f^b=fj,f^c=fj,f^d=fhj,f^e=fij,g^a=ghj,g^b=gj,g^d=gh,g^e=gij,h^a=hi,h^d=hi,h^f=hj,h^g=hj,i^d=ij

Conjugacy classes & character table

70 conjugacy classes — view the full character table.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from its polycyclic presentation:

gap> F := FreeGroup(IsSyllableWordsFamily, "a", "b", "c", "d", "e", "f", "g", "h", "i", "j");;
gap> coll := SingleCollector(F, [2, 2, 2, 2, 2, 2, 2, 2, 2, 2]);;
gap> SetPower(coll, 1, F.5);;
gap> SetPower(coll, 4, F.5*F.7);;
gap> SetPower(coll, 5, F.9);;
gap> SetPower(coll, 6, F.10);;
gap> SetPower(coll, 7, F.10);;
gap> SetPower(coll, 8, F.10);;
gap> SetConjugate(coll, 3, 1, F.3*F.9*F.10);;
gap> SetConjugate(coll, 3, 2, F.3*F.9*F.10);;
gap> SetConjugate(coll, 4, 1, F.4*F.6);;
gap> SetConjugate(coll, 4, 2, F.4*F.6*F.7*F.10);;
gap> SetConjugate(coll, 4, 3, F.4*F.10);;
gap> SetConjugate(coll, 5, 4, F.5*F.8);;
gap> SetConjugate(coll, 6, 1, F.6*F.8);;
gap> SetConjugate(coll, 6, 2, F.6*F.10);;
gap> SetConjugate(coll, 6, 3, F.6*F.10);;
gap> SetConjugate(coll, 6, 4, F.6*F.8*F.10);;
gap> SetConjugate(coll, 6, 5, F.6*F.9*F.10);;
gap> SetConjugate(coll, 7, 1, F.7*F.8*F.10);;
gap> SetConjugate(coll, 7, 2, F.7*F.10);;
gap> SetConjugate(coll, 7, 4, F.7*F.8);;
gap> SetConjugate(coll, 7, 5, F.7*F.9*F.10);;
gap> SetConjugate(coll, 8, 1, F.8*F.9);;
gap> SetConjugate(coll, 8, 4, F.8*F.9);;
gap> SetConjugate(coll, 8, 6, F.8*F.10);;
gap> SetConjugate(coll, 8, 7, F.8*F.10);;
gap> SetConjugate(coll, 9, 4, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);